Could I get into the Air Force being prior service in the Army, and having tattoos?

Both my wife and I have considered enlisting in the Air Force. I am more concerned about them accepting me though because I am prior service which I hear they do not like, and I have visible tattoos. I was honorably discharged from the Army about a month ago. I was a horizontal construction engineer in a combat engineer battalion. I was in Iraq for 15 months doing construction missions such as building new bases, and building additions to smaller ones, demolishing building, and filling IED craters with concrete. I also was a gun truck driver in many different tactical vehicles on convoys all over the country, and occasionally I was the gunner. I would of thought they would like the experience I have considering those jobs are much harder, and Army deployments are much longer so they know I could easily perform whatever task they throw my way. The other issue is a few visible tattoos. None of them are in anyway obscene, racist, or extremist, the Army was fine with them, but apparently the Air Force isn't too fond of ink. The visible ones are a celtic cross on my forearm, a celtic knot dragon on the other forearm, and a celtic knot shamrock on my left hand, the one I'm most concerned about. So basically what I'm wondering is would they allow a waiver for the tattoos, and would they prefer a brand new recruit that they can mold into an Airman, over me because I was a Soldier? Thanks for the help.